# Theta

The theta, $LaTeX: \Theta$, is the rate of change of the option price with time. It measures the time decay of an option:

$LaTeX: \Theta=\frac{\partial V}{\partial t}$.

At the start of the lifetime of a derivative, there is a potential for cashflows to occur in the future. As time progresses this potential decreases (eventually to zero), and theta is a measure of the rate of change of this decrease. Theta is related to the option value, the delta and the gamma by the Black-Scholes equation.

## References

• Taleb, NN 1997 Dynamic Hedging. John Wiley & Sons
• Wilmott, P 2001 Paul Wilmott Introduces Quantitative Finance. John Wiley & Sons
• Wilmott, P 2006 Frequently Asked Questions in Quantitative Finance. John Wiley & Sons